I've seen people on other forums say the main difference between older Minolta lenses and newer Sony, Sigma lenses are the coating for digital cameras. Does anyone know of any studies that talk about about this, or have thoughts from experience?

I'm no expert, but I did read Sony improved the coatings to give more contrast, whether this is because of the digital sensor, I don't know. Its also worth knowing that camera manufacturers colour match their lenses for colour uniformity, whether it be a wide angle or long tele. You often see a different colour on a picture during a slide show when a third party lens shot comes up. Also Canon discovered in the 35mm SLR days that high contrast coatings gave the impression of sharper images, I think this still holds true today.

I have seen some talk that, at least with some lenses, Sony's newer coatings have improved the performance of some of classic "previously-Minolta" lenses, in some cases by reducing that particular type of flare introduced by the interaction between the lens and digital sensor.

As I can't justify the prices Sony charge for their lenses, I can't offer a personal opinion except to say that it may, in this case, be more than just marketing.

I have, though, always been slightly curious to know whether the Sony re-badgings of Tamron and Minolta lenses really do generally improve on the originals, or whether any improvements are confined to specific lenses.

I can only speak as I find transiently, I prefer the colours on my KM 17-35 to my Sony 18-55 which is far too contrasty. I don't notice any flare problems unless I have the sun shining on the front element, but that's my fault not the lens, I use my KM and 24-85 M lenses on my A-37 and A6000 (soon to be sold) via an adaptor. I agree about Sony lens prices, especially E mount, hence the sale of my A6000. Yes, agreed that Sony have improved the performance of some of the inherited Minolta lenses, but not to every ones taste.